Analysis and finite element simulations of a second‐order fluid model in a bounded domain | Zendy

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Analysis and finite element simulations of a second‐order fluid model in a bounded domain

Author(s) -

Arada Nadir,

Correia Paulo,

Sequeira Adélia

Publication year - 2007

Publication title -

numerical methods for partial differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.901

H-Index - 61

eISSN - 1098-2426

pISSN - 0749-159X

DOI - 10.1002/num.20236

Subject(s) - mathematics , bounded function , finite element method , domain (mathematical analysis) , inertia , mathematical analysis , reynolds number , uniqueness , viscoelasticity , compressibility , partial differential equation , mechanics , classical mechanics , physics , turbulence , thermodynamics

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007

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